Cube Root Calculator

Number

Cube root —

Simplified radical —

Perfect cube? —

How to Simplify a Cube Root

Enter a number to get its cube root.

Enter the number

Type any number — cube roots of negatives are real, so −8 works.

Read the decimal root

The real cube root is shown first, rounded for display.

Read the radical form

For a whole number, the root is simplified by pulling out perfect-cube factors, like ∛54 = 3∛2.

Frequently Asked Questions

How do you simplify a cube root?

To simplify a cube root, factor out the largest perfect cube inside it. For ∛54, note that 54 = 27 × 2 and ∛27 = 3, so ∛54 = 3∛2. The same method gives ∛250 = ∛(125 × 2) = 5∛2. If no perfect-cube factor above 1 exists, as with ∛7, the root is already in its simplest form.

Can you take the cube root of a negative number?

Cube roots of negative numbers are perfectly ordinary real numbers, unlike square roots. Because a negative number cubed stays negative, ∛(−8) = −2 and ∛(−125) = −5. Every real number has exactly one real cube root, so there is no plus-or-minus ambiguity. Square roots differ because squaring always produces a non-negative result.

What is a perfect cube?

A perfect cube is a number whose cube root is a whole number, such as 27 (3³), 64 (4³) or 1000 (10³). The calculator tells you whether the value you entered is one. The first few perfect cubes are 1, 8, 27, 64, 125 and 216. Negative perfect cubes exist too, since (−4)³ = −64.

Is my data sent anywhere?

Nothing you enter into the cube root calculator leaves your device. The cube root calculator does all of its arithmetic client-side in JavaScript, so the number you enter are never uploaded to a server. No account is needed and no calculation is stored or logged. Once the page has loaded it works with no network connection at all.

Cube Root Calculator

How to Simplify a Cube Root

Enter the number

Read the decimal root

Read the radical form

Frequently Asked Questions

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